The analysis of transmission line tapers is approached through an integral equation formulation (equivalent to a series solution for propagation through an inhomogeneous medium given by Bremmer) which can be used to iteratively obtain approximations, the first of which is the formula ordinarily used in the analysis and synthesis problems. From the second, an estimation of the error involved in the computation of the reflection is obtained and studied in detail for the exponential and the Chebychev tapers. This latter is found to be very sensitive to the approximations involved far large mismatches and/or low residual reflections. Formulas and graphs are given that allow one to assess the accuracy and to improve the design.